Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(31,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.bl (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.31 |
Dual form | 2352.2.bl.n.607.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.12132 | + | 1.22474i | −0.948683 | + | 0.547723i | −0.892672 | − | 0.450708i | \(-0.851172\pi\) |
−0.0560116 | + | 0.998430i | \(0.517838\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12132 | + | 1.22474i | 0.639602 | + | 0.369274i | 0.784461 | − | 0.620178i | \(-0.212940\pi\) |
−0.144859 | + | 0.989452i | \(0.546273\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.89898i | − | 1.35873i | −0.733799 | − | 0.679366i | \(-0.762255\pi\) | ||
0.733799 | − | 0.679366i | \(-0.237745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.44949i | 0.632456i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.12132 | + | 1.22474i | 0.514496 | + | 0.297044i | 0.734680 | − | 0.678414i | \(-0.237332\pi\) |
−0.220184 | + | 0.975458i | \(0.570666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.36396 | + | 3.67423i | −1.32698 | + | 0.766131i | −0.984831 | − | 0.173516i | \(-0.944487\pi\) |
−0.342147 | + | 0.939647i | \(0.611154\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.718421 | − | 1.24434i | −0.243204 | − | 0.969975i | \(-0.578198\pi\) |
0.961625 | − | 0.274367i | \(-0.0884683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.12132 | − | 1.22474i | 0.369274 | − | 0.213201i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.24264 | − | 2.44949i | −0.679366 | − | 0.392232i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.34847i | 1.14764i | 0.818982 | + | 0.573819i | \(0.194539\pi\) | ||||
−0.818982 | + | 0.573819i | \(0.805461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.89898i | 0.747087i | 0.927613 | + | 0.373544i | \(0.121857\pi\) | ||||
−0.927613 | + | 0.373544i | \(0.878143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.12132 | + | 1.22474i | 0.316228 | + | 0.182574i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | − | 10.3923i | −0.875190 | − | 1.51587i | −0.856560 | − | 0.516047i | \(-0.827403\pi\) |
−0.0186297 | − | 0.999826i | \(-0.505930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.12132 | − | 1.22474i | 0.297044 | − | 0.171499i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | − | 10.3923i | 0.781133 | − | 1.35296i | −0.150148 | − | 0.988663i | \(-0.547975\pi\) |
0.931282 | − | 0.364299i | \(-0.118692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | + | 10.3923i | 0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.34847i | 0.884652i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.2474i | − | 1.45350i | −0.686900 | − | 0.726752i | \(-0.741029\pi\) | ||
0.686900 | − | 0.726752i | \(-0.258971\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.7279 | − | 7.34847i | −1.48969 | − | 0.860073i | −0.489760 | − | 0.871857i | \(-0.662916\pi\) |
−0.999931 | + | 0.0117840i | \(0.996249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.48528 | − | 4.89898i | 0.954669 | − | 0.551178i | 0.0601406 | − | 0.998190i | \(-0.480845\pi\) |
0.894528 | + | 0.447012i | \(0.147512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | − | 5.19615i | 0.321634 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6066 | − | 6.12372i | 1.12430 | − | 0.649113i | 0.181803 | − | 0.983335i | \(-0.441807\pi\) |
0.942495 | + | 0.334221i | \(0.108473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | − | 6.92820i | −0.414781 | − | 0.718421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.24264 | + | 2.44949i | 0.435286 | + | 0.251312i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.89898i | − | 0.497416i | −0.968579 | − | 0.248708i | \(-0.919994\pi\) | ||
0.968579 | − | 0.248708i | \(-0.0800060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.44949i | − | 0.246183i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.12132 | − | 1.22474i | −0.211079 | − | 0.121867i | 0.390734 | − | 0.920504i | \(-0.372221\pi\) |
−0.601813 | + | 0.798637i | \(0.705555\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | − | 13.8564i | −0.788263 | − | 1.36531i | −0.927030 | − | 0.374987i | \(-0.877647\pi\) |
0.138767 | − | 0.990325i | \(-0.455686\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.6066 | − | 6.12372i | 1.02538 | − | 0.592003i | 0.109721 | − | 0.993962i | \(-0.465004\pi\) |
0.915657 | + | 0.401960i | \(0.131671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.00000 | − | 15.5885i | 0.839254 | − | 1.45363i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.24264 | + | 2.44949i | −0.392232 | + | 0.226455i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.36396 | + | 3.67423i | 0.573819 | + | 0.331295i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 9.79796i | − | 0.876356i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.79796i | − | 0.869428i | −0.900568 | − | 0.434714i | \(-0.856849\pi\) | ||
0.900568 | − | 0.434714i | \(-0.143151\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.24264 | + | 2.44949i | 0.373544 | + | 0.215666i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.12132 | − | 1.22474i | 0.182574 | − | 0.105409i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.0000 | −1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | − | 10.3923i | 0.501745 | − | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.7279 | + | 7.34847i | −1.05700 | + | 0.610257i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.00000 | + | 15.5885i | 0.737309 | + | 1.27706i | 0.953703 | + | 0.300750i | \(0.0972370\pi\) |
−0.216394 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7279 | − | 7.34847i | −1.03578 | − | 0.598010i | −0.117147 | − | 0.993115i | \(-0.537375\pi\) |
−0.918636 | + | 0.395105i | \(0.870708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.44949i | − | 0.198030i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.5959i | 1.57398i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9706 | + | 9.79796i | 1.35440 | + | 0.781962i | 0.988862 | − | 0.148835i | \(-0.0475523\pi\) |
0.365536 | + | 0.930797i | \(0.380886\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9706 | + | 9.79796i | −1.32924 | + | 0.767435i | −0.985182 | − | 0.171514i | \(-0.945134\pi\) |
−0.344055 | + | 0.938949i | \(0.611801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.00000 | + | 5.19615i | −0.233550 | + | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | + | 1.73205i | −0.0764719 | + | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.36396 | + | 3.67423i | −0.483843 | + | 0.279347i | −0.722017 | − | 0.691876i | \(-0.756785\pi\) |
0.238174 | + | 0.971223i | \(0.423451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.00000 | − | 10.3923i | −0.450988 | − | 0.781133i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.8492 | − | 8.57321i | −1.10988 | − | 0.640792i | −0.171085 | − | 0.985256i | \(-0.554727\pi\) |
−0.938799 | + | 0.344464i | \(0.888061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.89898i | 0.364138i | 0.983286 | + | 0.182069i | \(0.0582795\pi\) | ||||
−0.983286 | + | 0.182069i | \(0.941721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.48528 | + | 4.89898i | 0.623850 | + | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.12132 | − | 1.22474i | 0.153493 | − | 0.0886194i | −0.421286 | − | 0.906928i | \(-0.638421\pi\) |
0.574779 | + | 0.818308i | \(0.305088\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.00000 | + | 13.8564i | −0.575853 | + | 0.997406i | 0.420096 | + | 0.907480i | \(0.361996\pi\) |
−0.995948 | + | 0.0899262i | \(0.971337\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | 0.859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00000 | + | 1.73205i | −0.0708881 | + | 0.122782i | −0.899291 | − | 0.437351i | \(-0.855917\pi\) |
0.828403 | + | 0.560133i | \(0.189250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | − | 15.5885i | −0.628587 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.36396 | + | 3.67423i | 0.442326 | + | 0.255377i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.89898i | − | 0.338869i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.89898i | − | 0.337260i | −0.985679 | − | 0.168630i | \(-0.946066\pi\) | ||
0.985679 | − | 0.168630i | \(-0.0539342\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.6066 | − | 6.12372i | −0.726752 | − | 0.419591i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.00000 | − | 10.3923i | −0.409197 | − | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7279 | + | 7.34847i | −0.860073 | + | 0.496564i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2132 | − | 12.2474i | 1.40181 | − | 0.809334i | 0.407230 | − | 0.913326i | \(-0.366495\pi\) |
0.994578 | + | 0.103992i | \(0.0331615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.0000 | + | 25.9808i | 0.982683 | + | 1.70206i | 0.651813 | + | 0.758380i | \(0.274009\pi\) |
0.330870 | + | 0.943676i | \(0.392658\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.4558 | + | 14.6969i | 1.66056 | + | 0.958723i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.79796i | − | 0.636446i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.2474i | 0.792222i | 0.918203 | + | 0.396111i | \(0.129640\pi\) | ||||
−0.918203 | + | 0.396111i | \(0.870360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.24264 | + | 2.44949i | 0.273293 | + | 0.157786i | 0.630383 | − | 0.776284i | \(-0.282898\pi\) |
−0.357090 | + | 0.934070i | \(0.616231\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.48528 | + | 4.89898i | −0.539906 | + | 0.311715i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.00000 | + | 5.19615i | −0.187867 | + | 0.325396i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.0919 | + | 11.0227i | −1.19092 | + | 0.687577i | −0.958515 | − | 0.285042i | \(-0.907992\pi\) |
−0.232404 | + | 0.972619i | \(0.574659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.12132 | + | 1.22474i | 0.130806 | + | 0.0755210i | 0.563975 | − | 0.825792i | \(-0.309271\pi\) |
−0.433169 | + | 0.901313i | \(0.642605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.6969i | 0.902826i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.2474i | − | 0.749532i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.0919 | − | 11.0227i | −1.16405 | − | 0.672066i | −0.211781 | − | 0.977317i | \(-0.567926\pi\) |
−0.952272 | + | 0.305251i | \(0.901260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.12132 | − | 1.22474i | 0.127920 | − | 0.0738549i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | − | 6.92820i | 0.240337 | − | 0.416275i | −0.720473 | − | 0.693482i | \(-0.756075\pi\) |
0.960810 | + | 0.277207i | \(0.0894088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.00000 | + | 12.1244i | −0.416107 | + | 0.720718i | −0.995544 | − | 0.0942988i | \(-0.969939\pi\) |
0.579437 | + | 0.815017i | \(0.303272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.24264 | − | 2.44949i | 0.251312 | − | 0.145095i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.50000 | − | 9.52628i | −0.323529 | − | 0.560369i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.24264 | − | 2.44949i | −0.248708 | − | 0.143592i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.0454i | 1.28791i | 0.765065 | + | 0.643953i | \(0.222707\pi\) | ||||
−0.765065 | + | 0.643953i | \(0.777293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.3939i | 1.71138i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.12132 | − | 1.22474i | −0.123091 | − | 0.0710669i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.0000 | + | 31.1769i | 1.04097 | + | 1.80301i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.12132 | + | 1.22474i | −0.121867 | + | 0.0703598i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0000 | 1.48390 | 0.741949 | − | 0.670456i | \(-0.233902\pi\) | ||||
0.741949 | + | 0.670456i | \(0.233902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | + | 20.7846i | −0.680458 | + | 1.17859i | 0.294384 | + | 0.955687i | \(0.404886\pi\) |
−0.974841 | + | 0.222900i | \(0.928448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.48528 | − | 4.89898i | 0.479616 | − | 0.276907i | −0.240640 | − | 0.970614i | \(-0.577357\pi\) |
0.720257 | + | 0.693708i | \(0.244024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.7279 | + | 7.34847i | 0.712627 | + | 0.411435i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 12.2474i | − | 0.683586i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.89898i | − | 0.272587i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.24264 | − | 2.44949i | −0.235339 | − | 0.135873i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.00000 | + | 1.73205i | 0.0553001 | + | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.2132 | − | 12.2474i | 1.16598 | − | 0.673181i | 0.213253 | − | 0.976997i | \(-0.431594\pi\) |
0.952731 | + | 0.303816i | \(0.0982610\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | + | 3.46410i | −0.109599 | + | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706 | − | 9.79796i | 0.919007 | − | 0.530589i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.00000 | − | 15.5885i | −0.484544 | − | 0.839254i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.8492 | − | 8.57321i | −0.797149 | − | 0.460234i | 0.0453242 | − | 0.998972i | \(-0.485568\pi\) |
−0.842473 | + | 0.538738i | \(0.818901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5959i | 1.04895i | 0.851427 | + | 0.524473i | \(0.175738\pi\) | ||||
−0.851427 | + | 0.524473i | \(0.824262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.89898i | 0.261488i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.12132 | − | 1.22474i | −0.112906 | − | 0.0651866i | 0.442483 | − | 0.896777i | \(-0.354098\pi\) |
−0.555390 | + | 0.831590i | \(0.687431\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.0000 | + | 25.9808i | 0.796117 | + | 1.37892i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.6066 | + | 6.12372i | −0.559795 | + | 0.323198i | −0.753063 | − | 0.657948i | \(-0.771425\pi\) |
0.193268 | + | 0.981146i | \(0.438091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.0000 | 1.88433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.00000 | + | 12.1244i | −0.365397 | + | 0.632886i | −0.988840 | − | 0.148983i | \(-0.952400\pi\) |
0.623443 | + | 0.781869i | \(0.285733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.36396 | − | 3.67423i | 0.331295 | − | 0.191273i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.48528 | − | 4.89898i | −0.438178 | − | 0.252982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 29.3939i | − | 1.51386i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 34.2929i | − | 1.76151i | −0.473576 | − | 0.880753i | \(-0.657037\pi\) | ||
0.473576 | − | 0.880753i | \(-0.342963\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.48528 | − | 4.89898i | −0.434714 | − | 0.250982i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00000 | − | 10.3923i | −0.306586 | − | 0.531022i | 0.671027 | − | 0.741433i | \(-0.265853\pi\) |
−0.977613 | + | 0.210411i | \(0.932520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.24264 | − | 2.44949i | 0.215666 | − | 0.124515i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0000 | + | 20.7846i | −0.603786 | + | 1.04579i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.48528 | + | 4.89898i | −0.425864 | + | 0.245873i | −0.697583 | − | 0.716504i | \(-0.745741\pi\) |
0.271719 | + | 0.962377i | \(0.412408\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.9411 | − | 19.5959i | −1.69073 | − | 0.976142i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 2.44949i | − | 0.121716i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.79796i | − | 0.485667i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.24264 | + | 2.44949i | 0.209785 | + | 0.121119i | 0.601212 | − | 0.799090i | \(-0.294685\pi\) |
−0.391426 | + | 0.920209i | \(0.628018\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00000 | + | 5.19615i | 0.147979 | + | 0.256307i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.00000 | − | 3.46410i | 0.0979404 | − | 0.169638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.0000 | 1.75872 | 0.879358 | − | 0.476162i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476162i | \(0.157972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.389896 | −0.194948 | − | 0.980814i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980814i | \(0.562454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | + | 10.3923i | −0.291730 | + | 0.505291i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.12132 | − | 1.22474i | 0.102899 | − | 0.0594089i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.00000 | − | 10.3923i | −0.289683 | − | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8492 | + | 8.57321i | 0.715263 | + | 0.412957i | 0.813007 | − | 0.582254i | \(-0.197829\pi\) |
−0.0977438 | + | 0.995212i | \(0.531163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.79796i | 0.470860i | 0.971891 | + | 0.235430i | \(0.0756498\pi\) | ||||
−0.971891 | + | 0.235430i | \(0.924350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.6969i | 0.704664i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.7279 | + | 7.34847i | 0.608859 | + | 0.351525i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.0000 | + | 19.0526i | 0.525001 | + | 0.909329i | 0.999576 | + | 0.0291138i | \(0.00926853\pi\) |
−0.474575 | + | 0.880215i | \(0.657398\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.12132 | − | 1.22474i | 0.100787 | − | 0.0581894i | −0.448759 | − | 0.893653i | \(-0.648134\pi\) |
0.549546 | + | 0.835463i | \(0.314801\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0000 | + | 25.9808i | −0.711068 | + | 1.23161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | + | 15.5885i | −0.423793 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.7279 | + | 7.34847i | −0.598010 | + | 0.345261i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0000 | − | 32.9090i | −0.888783 | − | 1.53942i | −0.841316 | − | 0.540544i | \(-0.818219\pi\) |
−0.0474665 | − | 0.998873i | \(-0.515115\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.12132 | − | 1.22474i | −0.0990148 | − | 0.0571662i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.44949i | − | 0.114084i | −0.998372 | − | 0.0570421i | \(-0.981833\pi\) | ||
0.998372 | − | 0.0570421i | \(-0.0181669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9.79796i | − | 0.455350i | −0.973737 | − | 0.227675i | \(-0.926888\pi\) | ||
0.973737 | − | 0.227675i | \(-0.0731123\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.9706 | + | 9.79796i | 0.786991 | + | 0.454369i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000 | + | 20.7846i | 0.555294 | + | 0.961797i | 0.997881 | + | 0.0650714i | \(0.0207275\pi\) |
−0.442587 | + | 0.896726i | \(0.645939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.9706 | − | 9.79796i | 0.781962 | − | 0.451466i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | + | 10.3923i | −0.275880 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | −0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.0000 | + | 20.7846i | −0.548294 | + | 0.949673i | 0.450098 | + | 0.892979i | \(0.351389\pi\) |
−0.998392 | + | 0.0566937i | \(0.981944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.9706 | + | 9.79796i | −0.773791 | + | 0.446748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | + | 10.3923i | 0.272446 | + | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.24264 | + | 2.44949i | 0.192252 | + | 0.110997i | 0.593037 | − | 0.805176i | \(-0.297929\pi\) |
−0.400784 | + | 0.916172i | \(0.631262\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.5959i | 0.886158i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 36.7423i | − | 1.65816i | −0.559131 | − | 0.829079i | \(-0.688865\pi\) | ||
0.559131 | − | 0.829079i | \(-0.311135\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.7279 | + | 7.34847i | 0.573237 | + | 0.330958i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | + | 5.19615i | 0.134840 | + | 0.233550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.7279 | − | 7.34847i | 0.569780 | − | 0.328963i | −0.187281 | − | 0.982306i | \(-0.559968\pi\) |
0.757061 | + | 0.653344i | \(0.226634\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | + | 10.3923i | −0.268060 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.50000 | + | 9.52628i | −0.244264 | + | 0.423077i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.8492 | + | 8.57321i | −0.658181 | + | 0.380001i | −0.791584 | − | 0.611061i | \(-0.790743\pi\) |
0.133402 | + | 0.991062i | \(0.457410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | + | 1.73205i | 0.0441511 | + | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.9411 | + | 19.5959i | 1.49562 | + | 0.863499i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 29.3939i | − | 1.29274i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.34847i | 0.322562i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.12132 | − | 1.22474i | −0.0929367 | − | 0.0536570i | 0.452811 | − | 0.891606i | \(-0.350421\pi\) |
−0.545748 | + | 0.837949i | \(0.683754\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | + | 17.3205i | 0.437269 | + | 0.757373i | 0.997478 | − | 0.0709788i | \(-0.0226123\pi\) |
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9706 | − | 9.79796i | 0.739249 | − | 0.426806i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.5000 | − | 26.8468i | 0.673913 | − | 1.16725i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.0000 | 1.55933 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0000 | + | 25.9808i | −0.648507 | + | 1.12325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.8492 | + | 8.57321i | −0.640792 | + | 0.369961i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.00000 | − | 13.8564i | −0.343947 | − | 0.595733i | 0.641215 | − | 0.767361i | \(-0.278431\pi\) |
−0.985162 | + | 0.171628i | \(0.945097\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.24264 | + | 2.44949i | 0.182069 | + | 0.105118i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.89898i | − | 0.209849i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3939i | 1.25679i | 0.777894 | + | 0.628396i | \(0.216288\pi\) | ||||
−0.777894 | + | 0.628396i | \(0.783712\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | − | 10.3923i | −0.255609 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.48528 | − | 4.89898i | 0.360180 | − | 0.207950i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.00000 | + | 5.19615i | −0.127114 | + | 0.220168i | −0.922557 | − | 0.385860i | \(-0.873905\pi\) |
0.795443 | + | 0.606028i | \(0.207238\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00000 | 0.253320 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0000 | + | 20.7846i | −0.505740 | + | 0.875967i | 0.494238 | + | 0.869326i | \(0.335447\pi\) |
−0.999978 | + | 0.00664037i | \(0.997886\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.7279 | + | 7.34847i | −0.535468 | + | 0.309152i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.9706 | − | 9.79796i | −0.710196 | − | 0.410032i | 0.100938 | − | 0.994893i | \(-0.467816\pi\) |
−0.811134 | + | 0.584861i | \(0.801149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.44949i | − | 0.102329i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.34847i | 0.306452i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.00000 | + | 13.8564i | 0.332469 | + | 0.575853i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.7279 | − | 7.34847i | 0.527137 | − | 0.304342i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | − | 10.3923i | 0.248069 | − | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | − | 15.5885i | 0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.3051 | − | 23.2702i | 1.65513 | − | 0.955591i | 0.680217 | − | 0.733011i | \(-0.261886\pi\) |
0.974914 | − | 0.222580i | \(-0.0714478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.00000 | + | 1.73205i | 0.0409273 | + | 0.0708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.12132 | + | 1.22474i | 0.0866748 | + | 0.0500417i | 0.542711 | − | 0.839920i | \(-0.317398\pi\) |
−0.456036 | + | 0.889961i | \(0.650731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.5959i | − | 0.799334i | −0.916660 | − | 0.399667i | \(-0.869126\pi\) | ||
0.916660 | − | 0.399667i | \(-0.130874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.6066 | + | 6.12372i | 0.431220 | + | 0.248965i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.00000 | − | 12.1244i | −0.284121 | − | 0.492112i | 0.688274 | − | 0.725450i | \(-0.258368\pi\) |
−0.972396 | + | 0.233338i | \(0.925035\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −50.9117 | + | 29.3939i | −2.05967 | + | 1.18915i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0000 | + | 22.5167i | −0.525065 | + | 0.909439i | 0.474509 | + | 0.880251i | \(0.342626\pi\) |
−0.999574 | + | 0.0291886i | \(0.990708\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0000 | −0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.0000 | −1.69086 | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.00000 | + | 3.46410i | −0.0803868 | + | 0.139234i | −0.903416 | − | 0.428765i | \(-0.858949\pi\) |
0.823029 | + | 0.567999i | \(0.192282\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.36396 | − | 3.67423i | 0.255377 | − | 0.147442i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.24264 | − | 2.44949i | −0.169435 | − | 0.0978232i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.79796i | − | 0.390670i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5959i | 0.780101i | 0.920793 | + | 0.390051i | \(0.127542\pi\) | ||||
−0.920793 | + | 0.390051i | \(0.872458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.24264 | − | 2.44949i | −0.168630 | − | 0.0973585i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.0000 | + | 20.7846i | 0.476205 | + | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.6066 | + | 6.12372i | −0.419591 | + | 0.242251i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.00000 | − | 5.19615i | 0.118493 | − | 0.205236i | −0.800678 | − | 0.599095i | \(-0.795527\pi\) |
0.919171 | + | 0.393860i | \(0.128860\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0000 | 0.552106 | 0.276053 | − | 0.961142i | \(-0.410973\pi\) | ||||
0.276053 | + | 0.961142i | \(0.410973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0000 | −0.472500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | + | 20.7846i | −0.471769 | + | 0.817127i | −0.999478 | − | 0.0322975i | \(-0.989718\pi\) |
0.527710 | + | 0.849425i | \(0.323051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.4558 | − | 14.6969i | 0.999229 | − | 0.576905i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6969i | 0.573382i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 7.34847i | − | 0.286256i | −0.989704 | − | 0.143128i | \(-0.954284\pi\) | ||
0.989704 | − | 0.143128i | \(-0.0457160\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.4558 | − | 14.6969i | −0.990118 | − | 0.571645i | −0.0848081 | − | 0.996397i | \(-0.527028\pi\) |
−0.905309 | + | 0.424753i | \(0.860361\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.00000 | − | 10.3923i | −0.233021 | − | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.1838 | + | 22.0454i | −1.47848 | + | 0.853602i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.00000 | + | 8.66025i | −0.193311 | + | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.00000 | −0.308377 | −0.154189 | − | 0.988041i | \(-0.549276\pi\) | ||||
−0.154189 | + | 0.988041i | \(0.549276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.6066 | + | 6.12372i | −0.407645 | + | 0.235354i | −0.689777 | − | 0.724022i | \(-0.742292\pi\) |
0.282132 | + | 0.959375i | \(0.408958\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | − | 10.3923i | −0.229920 | − | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.36396 | + | 3.67423i | 0.243510 | + | 0.140591i | 0.616789 | − | 0.787129i | \(-0.288433\pi\) |
−0.373279 | + | 0.927719i | \(0.621767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14.6969i | − | 0.561541i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 24.4949i | − | 0.934539i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.4558 | − | 14.6969i | −0.969790 | − | 0.559909i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | + | 17.3205i | 0.380418 | + | 0.658903i | 0.991122 | − | 0.132956i | \(-0.0424468\pi\) |
−0.610704 | + | 0.791859i | \(0.709113\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.48528 | + | 4.89898i | −0.321865 | + | 0.185829i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.0000 | 1.13470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | + | 6.92820i | −0.150863 | + | 0.261302i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.4558 | − | 14.6969i | 0.958723 | − | 0.553519i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.48528 | − | 4.89898i | −0.318223 | − | 0.183726i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58.7878i | 2.20162i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.3939i | 1.09927i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.6066 | + | 6.12372i | 0.396111 | + | 0.228695i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0000 | + | 20.7846i | 0.447524 | + | 0.775135i | 0.998224 | − | 0.0595683i | \(-0.0189724\pi\) |
−0.550700 | + | 0.834703i | \(0.685639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.24264 | − | 2.44949i | 0.157786 | − | 0.0910975i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | − | 5.19615i | 0.111417 | − | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.00000 | + | 10.3923i | −0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.24264 | + | 2.44949i | −0.156706 | + | 0.0904740i | −0.576302 | − | 0.817237i | \(-0.695505\pi\) |
0.419597 | + | 0.907711i | \(0.362172\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.48528 | + | 4.89898i | 0.312136 | + | 0.180212i | 0.647882 | − | 0.761741i | \(-0.275655\pi\) |
−0.335746 | + | 0.941953i | \(0.608988\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.79796i | 0.359937i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.2474i | 0.449315i | 0.974438 | + | 0.224658i | \(0.0721264\pi\) | ||||
−0.974438 | + | 0.224658i | \(0.927874\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.1838 | − | 22.0454i | −1.39894 | − | 0.807681i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.6985 | + | 17.1464i | −1.08371 | + | 0.625682i | −0.931896 | − | 0.362726i | \(-0.881846\pi\) |
−0.151817 | + | 0.988409i | \(0.548513\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.0000 | 1.31017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | + | 15.5885i | −0.326679 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.0624 | + | 20.8207i | −1.30726 | + | 0.754748i | −0.981638 | − | 0.190751i | \(-0.938908\pi\) |
−0.325624 | + | 0.945499i | \(0.605574\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.00000 | + | 5.19615i | 0.108465 | + | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.9117 | − | 29.3939i | −1.83831 | − | 1.06135i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.79796i | 0.353323i | 0.984272 | + | 0.176662i | \(0.0565299\pi\) | ||||
−0.984272 | + | 0.176662i | \(0.943470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0454i | 0.793946i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.0919 | + | 11.0227i | 0.686687 | + | 0.396459i | 0.802370 | − | 0.596827i | \(-0.203572\pi\) |
−0.115683 | + | 0.993286i | \(0.536906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | − | 6.92820i | −0.143684 | − | 0.248868i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.7279 | − | 7.34847i | 0.456025 | − | 0.263286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0000 | − | 25.9808i | 0.536742 | − | 0.929665i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.00000 | −0.214423 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.0000 | −1.71319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.0000 | − | 17.3205i | 0.356462 | − | 0.617409i | −0.630905 | − | 0.775860i | \(-0.717316\pi\) |
0.987367 | + | 0.158450i | \(0.0506498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.12132 | − | 1.22474i | 0.0755210 | − | 0.0436021i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.7279 | + | 7.34847i | 0.451413 | + | 0.260623i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.7423i | 1.30148i | 0.759300 | + | 0.650740i | \(0.225541\pi\) | ||||
−0.759300 | + | 0.650740i | \(0.774459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 29.3939i | − | 1.03988i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6066 | − | 6.12372i | −0.374766 | − | 0.216371i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0000 | − | 31.1769i | −0.635206 | − | 1.10021i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.0919 | + | 11.0227i | −0.672066 | + | 0.388018i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | + | 15.5885i | −0.316423 | + | 0.548061i | −0.979739 | − | 0.200279i | \(-0.935815\pi\) |
0.663316 | + | 0.748340i | \(0.269149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0000 | − | 41.5692i | 0.840683 | − | 1.45611i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.48528 | − | 4.89898i | 0.296862 | − | 0.171394i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | − | 15.5885i | −0.314102 | − | 0.544041i | 0.665144 | − | 0.746715i | \(-0.268370\pi\) |
−0.979246 | + | 0.202674i | \(0.935037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.9706 | + | 9.79796i | 0.591557 | + | 0.341535i | 0.765713 | − | 0.643183i | \(-0.222386\pi\) |
−0.174156 | + | 0.984718i | \(0.555720\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.44949i | − | 0.0852803i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.5403i | 1.61836i | 0.587557 | + | 0.809182i | \(0.300090\pi\) | ||||
−0.587557 | + | 0.809182i | \(0.699910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.24264 | + | 2.44949i | 0.147353 | + | 0.0850743i | 0.571864 | − | 0.820349i | \(-0.306221\pi\) |
−0.424511 | + | 0.905423i | \(0.639554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | − | 6.92820i | −0.138758 | − | 0.240337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.4558 | − | 14.6969i | 0.880936 | − | 0.508609i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | + | 6.92820i | −0.138260 | + | 0.239474i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.00000 | − | 5.19615i | 0.103325 | − | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.3345 | − | 13.4722i | 0.802732 | − | 0.463458i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.00000 | + | 12.1244i | 0.240239 | + | 0.416107i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.4558 | + | 14.6969i | 0.872615 | + | 0.503805i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 29.3939i | − | 1.00643i | −0.864162 | − | 0.503214i | \(-0.832151\pi\) | ||
0.864162 | − | 0.503214i | \(-0.167849\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4.89898i | − | 0.167542i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0919 | + | 11.0227i | 0.652166 | + | 0.376528i | 0.789286 | − | 0.614026i | \(-0.210451\pi\) |
−0.137119 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0000 | + | 19.0526i | 0.375315 | + | 0.650065i | 0.990374 | − | 0.138416i | \(-0.0442012\pi\) |
−0.615059 | + | 0.788481i | \(0.710868\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.5477 | − | 25.7196i | 1.51642 | − | 0.875507i | 0.516608 | − | 0.856222i | \(-0.327194\pi\) |
0.999814 | − | 0.0192849i | \(-0.00613896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | − | 15.5885i | 0.306009 | − | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.0000 | −0.373580 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.24264 | + | 2.44949i | −0.143592 | + | 0.0829027i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0000 | + | 19.0526i | 0.371444 | + | 0.643359i | 0.989788 | − | 0.142548i | \(-0.0455296\pi\) |
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.0919 | + | 11.0227i | 0.643953 | + | 0.371787i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.44949i | 0.0825254i | 0.999148 | + | 0.0412627i | \(0.0131381\pi\) | ||||
−0.999148 | + | 0.0412627i | \(0.986862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34.2929i | − | 1.15405i | −0.816728 | − | 0.577023i | \(-0.804214\pi\) | ||
0.816728 | − | 0.577023i | \(-0.195786\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.4558 | + | 14.6969i | 0.855689 | + | 0.494032i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.00000 | + | 10.3923i | 0.201460 | + | 0.348939i | 0.948999 | − | 0.315279i | \(-0.102098\pi\) |
−0.747539 | + | 0.664218i | \(0.768765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.12132 | + | 1.22474i | −0.0710669 | + | 0.0410305i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0000 | + | 20.7846i | −0.401565 | + | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.0000 | 1.40391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.0000 | 1.20201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.0000 | − | 41.5692i | 0.800445 | − | 1.38641i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.7279 | − | 7.34847i | 0.424029 | − | 0.244813i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.00000 | − | 10.3923i | −0.199447 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.2132 | + | 12.2474i | 0.704373 | + | 0.406670i | 0.808974 | − | 0.587844i | \(-0.200023\pi\) |
−0.104601 | + | 0.994514i | \(0.533357\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.44949i | 0.0812444i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.34847i | 0.243466i | 0.992563 | + | 0.121733i | \(0.0388451\pi\) | ||||
−0.992563 | + | 0.121733i | \(0.961155\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.7279 | − | 7.34847i | 0.419855 | − | 0.242404i | −0.275160 | − | 0.961398i | \(-0.588731\pi\) |
0.695015 | + | 0.718995i | \(0.255398\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.0000 | − | 22.5167i | 0.428365 | − | 0.741949i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.0000 | −1.97492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | + | 13.8564i | −0.262754 | + | 0.455104i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6066 | + | 6.12372i | −0.347991 | + | 0.200913i | −0.663800 | − | 0.747910i | \(-0.731057\pi\) |
0.315809 | + | 0.948823i | \(0.397724\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.0000 | + | 20.7846i | 0.392862 | + | 0.680458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.7279 | − | 7.34847i | −0.416248 | − | 0.240321i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39.1918i | − | 1.28034i | −0.768233 | − | 0.640171i | \(-0.778864\pi\) | ||
0.768233 | − | 0.640171i | \(-0.221136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 9.79796i | − | 0.319744i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.6066 | + | 6.12372i | 0.345765 | + | 0.199628i | 0.662819 | − | 0.748780i | \(-0.269360\pi\) |
−0.317053 | + | 0.948408i | \(0.602693\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.0000 | − | 46.7654i | −0.879241 | − | 1.52289i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.3345 | − | 13.4722i | 0.758270 | − | 0.437787i | −0.0704042 | − | 0.997519i | \(-0.522429\pi\) |
0.828674 | + | 0.559731i | \(0.189096\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.0000 | + | 62.3538i | −1.16861 | + | 2.02409i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.00000 | + | 5.19615i | −0.0970777 | + | 0.168144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.7279 | − | 7.34847i | 0.411435 | − | 0.237542i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.6066 | − | 6.12372i | −0.341793 | − | 0.197334i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 39.1918i | − | 1.26163i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 58.7878i | − | 1.89049i | −0.326366 | − | 0.945243i | \(-0.605824\pi\) | ||
0.326366 | − | 0.945243i | \(-0.394176\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.24264 | − | 2.44949i | −0.136293 | − | 0.0786889i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | − | 31.1769i | −0.577647 | − | 1.00051i | −0.995748 | − | 0.0921142i | \(-0.970638\pi\) |
0.418101 | − | 0.908401i | \(-0.362696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.24264 | + | 2.44949i | −0.135873 | + | 0.0784465i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.00000 | + | 5.19615i | −0.0959785 | + | 0.166240i | −0.910017 | − | 0.414572i | \(-0.863931\pi\) |
0.814038 | + | 0.580812i | \(0.197265\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.0000 | 0.958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.00000 | − | 10.3923i | 0.191370 | − | 0.331463i | −0.754334 | − | 0.656490i | \(-0.772040\pi\) |
0.945705 | + | 0.325027i | \(0.105374\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.1838 | + | 22.0454i | −1.21664 | + | 0.702425i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.0000 | − | 31.1769i | −0.572367 | − | 0.991368i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7279 | − | 7.34847i | −0.404316 | − | 0.233432i | 0.284029 | − | 0.958816i | \(-0.408329\pi\) |
−0.688344 | + | 0.725384i | \(0.741662\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 24.4949i | − | 0.777322i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.89898i | − | 0.155308i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.00000 | + | 3.46410i | 0.0632772 | + | 0.109599i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2352.2.bl.n.31.1 | 4 | ||
4.3 | odd | 2 | 2352.2.bl.m.31.1 | 4 | |||
7.2 | even | 3 | inner | 2352.2.bl.n.607.2 | 4 | ||
7.3 | odd | 6 | 336.2.b.c.223.2 | yes | 2 | ||
7.4 | even | 3 | 336.2.b.b.223.1 | ✓ | 2 | ||
7.5 | odd | 6 | 2352.2.bl.m.607.1 | 4 | |||
7.6 | odd | 2 | 2352.2.bl.m.31.2 | 4 | |||
21.11 | odd | 6 | 1008.2.b.e.559.2 | 2 | |||
21.17 | even | 6 | 1008.2.b.d.559.1 | 2 | |||
28.3 | even | 6 | 336.2.b.b.223.2 | yes | 2 | ||
28.11 | odd | 6 | 336.2.b.c.223.1 | yes | 2 | ||
28.19 | even | 6 | inner | 2352.2.bl.n.607.1 | 4 | ||
28.23 | odd | 6 | 2352.2.bl.m.607.2 | 4 | |||
28.27 | even | 2 | inner | 2352.2.bl.n.31.2 | 4 | ||
56.3 | even | 6 | 1344.2.b.d.895.1 | 2 | |||
56.11 | odd | 6 | 1344.2.b.a.895.2 | 2 | |||
56.45 | odd | 6 | 1344.2.b.a.895.1 | 2 | |||
56.53 | even | 6 | 1344.2.b.d.895.2 | 2 | |||
84.11 | even | 6 | 1008.2.b.d.559.2 | 2 | |||
84.59 | odd | 6 | 1008.2.b.e.559.1 | 2 | |||
168.11 | even | 6 | 4032.2.b.d.3583.1 | 2 | |||
168.53 | odd | 6 | 4032.2.b.f.3583.1 | 2 | |||
168.59 | odd | 6 | 4032.2.b.f.3583.2 | 2 | |||
168.101 | even | 6 | 4032.2.b.d.3583.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.b.b.223.1 | ✓ | 2 | 7.4 | even | 3 | ||
336.2.b.b.223.2 | yes | 2 | 28.3 | even | 6 | ||
336.2.b.c.223.1 | yes | 2 | 28.11 | odd | 6 | ||
336.2.b.c.223.2 | yes | 2 | 7.3 | odd | 6 | ||
1008.2.b.d.559.1 | 2 | 21.17 | even | 6 | |||
1008.2.b.d.559.2 | 2 | 84.11 | even | 6 | |||
1008.2.b.e.559.1 | 2 | 84.59 | odd | 6 | |||
1008.2.b.e.559.2 | 2 | 21.11 | odd | 6 | |||
1344.2.b.a.895.1 | 2 | 56.45 | odd | 6 | |||
1344.2.b.a.895.2 | 2 | 56.11 | odd | 6 | |||
1344.2.b.d.895.1 | 2 | 56.3 | even | 6 | |||
1344.2.b.d.895.2 | 2 | 56.53 | even | 6 | |||
2352.2.bl.m.31.1 | 4 | 4.3 | odd | 2 | |||
2352.2.bl.m.31.2 | 4 | 7.6 | odd | 2 | |||
2352.2.bl.m.607.1 | 4 | 7.5 | odd | 6 | |||
2352.2.bl.m.607.2 | 4 | 28.23 | odd | 6 | |||
2352.2.bl.n.31.1 | 4 | 1.1 | even | 1 | trivial | ||
2352.2.bl.n.31.2 | 4 | 28.27 | even | 2 | inner | ||
2352.2.bl.n.607.1 | 4 | 28.19 | even | 6 | inner | ||
2352.2.bl.n.607.2 | 4 | 7.2 | even | 3 | inner | ||
4032.2.b.d.3583.1 | 2 | 168.11 | even | 6 | |||
4032.2.b.d.3583.2 | 2 | 168.101 | even | 6 | |||
4032.2.b.f.3583.1 | 2 | 168.53 | odd | 6 | |||
4032.2.b.f.3583.2 | 2 | 168.59 | odd | 6 |